﻿<p>The <em>IfcSphericalSurface</em> is a bounded elementary surface. The inherited <em>Position</em> attribute defines the
<em>IfcAxisPlacement3D</em> and provides:</p>
<ul>
<li><em>SELF\IfcElementarySurface.Position</em>: The location and orientation of the axis system for the
primitive.&nbsp;</li>
<li><em>SELF\IfcElementarySurface.Position.Location</em>: The center of the spherical surface.</li>
<li><em>SELF\IfcElementarySurface.Position.Position[3]:</em> The z axis points at its positve direction towards the north
pole, and by its negative directions towards the south pole.</li>
</ul>

<blockquote class="extDef">NOTE&nbsp; Definition according to ISO/CD 10303-42:1992<br>
<p style="font-size:inherit">An <em>IfcSphericalSurface</em> is a type of an elementary surface, which is at a constant distance (the <b>radius</b>) from a central point. A spherical surface is defined by the radius and the location and orientation of the surface.</p>
<p style="font-size:inherit"> The data is to be interpreted as follows: </p> 
<blockquote style="font-size:inherit">
C = Position.Location<br>
x = Position.P[1]<br>
y = Position.P[2]<br>
z = Position.P[3] (axis of spherical surface)<br>
<em>R</em> = Radius
</blockquote>    
<p style="font-size:inherit">and the surface is parametrised as </p>
<blockquote style="font-size:inherit"><i><b>&#963;</b>(u,v)</i> = <b>C</b> + R cos <i>v</i> ((cos <i>u</i>) <b>x</b> + (sin <i>u</i>) <b>y</b>) + R(sin <i>v</i>) <b>z</b> 
</blockquote>
<p style="font-size:inherit">where the parametrisation range is <i>0 &#8804; u &#8804; 360</i> degrees and <i>-90 &#8804; v &#8804; 90</i> degrees. <i>u</i> and <i>v</i> are angular parameters and when numerical values are specified they shall use the current units for plane angle measure.</p> 
<p style="font-size:inherit">In the placement coordinate system defined above, the surface is represented by the equation <i>S</i> = 0, where</p>
<blockquote style="font-size:inherit"><i> S(x, y, z) = x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> - R<sup>2</sup>.  </i>
</blockquote>
<p style="font-size:inherit">The positive direction of the normal to the surface at any point on the surface is given by</p>
<blockquote style="font-size:inherit"><i>(S<sub>x</sub>, S<sub>y</sub>, S<sub>z</sub> ).</i>
</blockquote>
<p style="font-size:inherit">The unit normal is given by </p>
<blockquote style="font-size:inherit"><b>N</b><i>(u,v)</i> = cos <i>v</i>((cos <i>u</i>)<b>x</b> + (sin <i>u</i>)<b>y</b>) + (sin <i>v</i>)<b>z</b>,
</blockquote>
</blockquote>

<blockquote class="note">NOTE&nbsp; Entity adapted from <strong>spherical_surface</strong> defined in ISO 10303-42.</blockquote>
<blockquote class="history">HISTORY&nbsp; New entity in IFC4 Addendum 2.</blockquote>